(2) Symmetry: the symmetry of hyperbola is exactly the same as that of ellipse, and it is symmetrical about X axis, Y axis and origin center.

(3) Vertices: two vertices A 1(-a, 0), A2(a, 0). The line segment between the two vertices is a real axis with a length of 2a and an imaginary axis with a length of 2b, c2=a2+b2. It is different from an ellipse.

(4) Asymptote: the unique property of hyperbola, equation Y = (b/a) x (when the focus is on the X axis), Y = (a/b) x (when the focus is on the Y axis) or let hyperbola x 2/a 2-y 2/b 2 =1.

(5) Eccentricity e> 1, with the increase of e, the hyperbolic opening gradually widens.

(6) equilateral hyperbola (equilateral hyperbola): x 2-y 2 = c, where C≠0 and its eccentricity e=c/a=√2.

(7)*** Yoke hyperbola: The equation X 2/A 2-Y 2/B 2 = 1 is the same as the hyperbola * * represented by X 2/A 2-Y 2/B 2 =- 1, and both have * * * yokes.

2. where ellipse =1(a >; B & gt0)*** The focal curve system equation can be expressed as -= 1(λ0 is an ellipse, B2.

2. The second definition of hyperbola

The ratio of the distance to the fixed point F(c, 0) to the distance to the fixed straight line L in the plane: x=+(-)a2/c is equal to the constant E = C/A (C > The locus of point a>0 is a hyperbola, the fixed point is the focus of hyperbola, the fixed line is the directrix of hyperbola, and the focal length (focal parameter) p= is the same as that of an ellipse.

3. When the focal radius (-= 1, F 1(-c, 0), F2(c, 0)) and point p(x0, y0) are on the right branch of hyperbola -= 1, | pf1| =

P, then | pf1| = ex1+a | pf2 | = ex1-a.